Convex duality and applications in mass transport and calculus of variations"

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Convexity and the theory of convex duality is at the heart of modern numerical methods to solve efficiently optimization problems arising in applied contexts such as image processing or machine learning. The optimal mass transportation problem also illustrates how powerful this theory can be and is a particularly active field of modern research. These lectures will cover in details convex duality theory and its use in optimization, the calculus of variations and mass transportation problems.